A simplified general relativistic model to analyze the structure of spiral galaxies
Un modèle simplifié basé sur la relativité générale pour analyser la structure des galaxies spirales
Résumé
The aim of this article is to develop a model able to investigate the interest to consider general relativistic effects when analyzing the structure of spiral galaxies. It is stressed that the aim is not to explain the flat rotation curve of spiral galaxies without dark matter.
With respect to the usual approach, which consists in relying on the Newton's law of gravitation, the main difference is the fact that this new model uses the theory of general relativity. In particular, we determine the analytical stationary solution of an axisymmetric rotating pressureless fluid for the linearized equations of the theory of general relativity. The development of this new model is motivated by the fact that since the Newton's law of gravitation is a coarser approximation of general relativity than its linear approximation, we may hope that the new model will allow to have a better understanding of the physics of spiral galaxies.
We demonstrate that the model leads to some constraints on the rotation curve. In particular, the positiveness of the density imposes the rotation curve to be flat in the regions where the density and general relativistic effects are small, such as in the disk region. So by considering a general relativistic model, we show that the expected profile in the disk region is a flat rotation curve, and not the Keplerian profile.
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